A conference key distribution system based on the Lagrange interpolating polynomial

A conference key distribution system (CKDS) can provide a common secret communication key to a set of M stations. A CKDS based on Lagrange interpolating polynomial is introduced. It is easy to see that breaking this system is equivalent to break the Diffie-Hellman public-key distribution system. This conference key is selected by the conference chairstation and hidden in the Lagrange interpolating polynomial. Recovering this key by each participating station only requires M-1 multiplications and M-2 additions over a finite field GF(P).< >